# What is the difference between PRF and a Random Oracle?

What is the difference between Pseudo Random Functions and Random Oracles?

1. Is the difference only about the domain of PRFs and Random Oracles, former having a fixed domain and latter can act on any input as long as it is well formatted?
2. Having a Random Oracle is a stronger assumption, why is that?
• Take a look at this for an intuitive definition of the random oracle – rath Apr 4 '14 at 0:34

1. $\;\;\;$ No. $\:$ A PRF involves a secret key; a Random Oracle doesn't.

2. $\;\;\;$ One can construct a PRF from a random oracle.

• I'm not sure of 2), because a PRF is supposed to have a circuit representation (and it's a strong property). – Ievgeni Sep 20 '19 at 12:20

Random oracles are purely random. They don't involve any cryptographic functions. They could be considered as the set of all functions that map an input to output. In that sense, a PRF could be considered a subset. Random oracles are stronger assumptions because they are totally random. The measure of a secure PRF is how indistinguishable it's from a Random Oracle. The more indistinguishable the better.